We present Chain of Simulation (CoS), a novel dual-mode reasoning framework that dynamically routes problems to specialized reasoning strategies in Large Language Models (LLMs). Unlike existing uniform prompting approaches, CoS employs three distinct reasoning modes: (1) computational flow with self-consistency for mathematical problems, (2) symbolic state tracking with JSON representations for spatial reasoning, and (3) hybrid fact-extraction for multi-hop inference. Through comprehensive evaluation on GSM8K, StrategyQA, and bAbI benchmarks using four state-of-the-art models (Gemma-3 27B, LLaMA-3.1 8B, Mistral 7B, and Qwen-2.5 14B), we demonstrate that CoS achieves 71.5% accuracy on GSM8K (1.0% absolute improvement), 90.0% on StrategyQA (2.5% improvement), and 19.0% on bAbI (65.2% relative improvement) compared to the strongest baselines. The analysis reveals that problem-specific mode selection is crucial, with computational mode achieving 81.2% accuracy when correctly applied to mathematical problems, while misrouting leads to 0% accuracy. We provide detailed algorithms for mode selection, state tracking, and answer extraction, establishing CoS as an effective approach for improving LLM reasoning without additional training. The framework provides superior trade-offs between accuracy and efficiency compared to Self-Consistency, achieving comparable performance at 54% lower computational cost.